Time-limited and k-limited polling systems: a matrix analytic solution

Ahmad Al Hanbali, Roland de Haan, Richardus J. Boucherie, Jan C.W. van Ommeren

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Abstract

In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.
Original languageUndefined
Title of host publicationThe 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools)
Place of PublicationGent, Belgium
PublisherICST
Pages-
Number of pages10
ISBN (Print)978-963-9799-31-8
DOIs
Publication statusPublished - 2008

Publication series

Name
PublisherInstitute for Computer Sciences, Social-Informatics and Telecommunications Engineering (ICST)
NumberCFP08545-D

Keywords

  • EWI-14667
  • METIS-255032
  • IR-65239

Cite this

Al Hanbali, A., de Haan, R., Boucherie, R. J., & van Ommeren, J. C. W. (2008). Time-limited and k-limited polling systems: a matrix analytic solution. In The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools) (pp. -). Gent, Belgium: ICST. https://doi.org/10.4108/ICST.VALUETOOLS2008.4378